On a new integration rule with the Gegenbauer polynomials for singular integral equations used in the theory of elasticity

1988 ◽  
Vol 58 (1) ◽  
pp. 35-46 ◽  
Author(s):  
E. G. Ladopoulos
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Theory Of Elasticity ◽  
Gegenbauer Polynomials ◽  
Integration Rule

scholarly journals CUBIC MECHANICAL METHOD FOR THE NONLINEAR SYSTEM OF SINGULAR INTEGRAL EQUATIONS

1990 ◽  
Vol 21 (3) ◽  
pp. 201-209
Author(s):  
R. P. Eissa ◽  
M. M. Gad
Keyword(s):  
Approximate Solution ◽  
Nonlinear System ◽  
Integral Equations ◽  
Nonlinear Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Original System ◽  
Theory Of Elasticity ◽  
Discrete Operator ◽  
Mechanical Method

Many applied problems in the theory of elasticity can be reduced to the solution of singular integral equations either linear or nonlinear. In this paper we shall study a nonlinear system of singular integral equations which appear on the closed Lipanouv surface in an ideal medium [4]. We shall find a cubic mechanical method which corresponds to the system and prove its convergence; we obtained a discrete operator which corresponds to this system and study its properties and then a solution to the resulting system of the nonlinear equations which leads to an approximate solution for the original system and its convergence.

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